Spatial Allocation of Elderly Care Resources in High-Density Urban Areas Under the Guidance of Efficiency and Equity

Rapid urban population aging and increasing land constraints pose significant challenges for improving both service coverage and spatial equity in elderly care facility planning. This study develops an integrated optimization framework that simultaneously addresses accessibility, efficiency, and equity in the spatial allocation of elderly care facilities. First, an improved Gaussian Two-Step Floating Catchment Area (G2SFCA) method is employed to evaluate accessibility patterns across multiple facility types under both walking and driving scenarios. Second, resource allocation equity is quantified using Lorenz curves and spatial Gini coefficients to identify mismatches between elderly care supply and population demand. Building upon these analyses, a fairness-oriented maximum covering location model—termed the Equity Maximum Covering Location Problem (EMCLP)—is formulated and further transformed into a Markov Decision Process. A deep reinforcement learning-based algorithm is subsequently designed to solve the EMCLP under complex spatial constraints. Experiment results demonstrate that the proposed approach achieves improved computational efficiency while maintaining robust solution quality, and effectively enhances service provision in underserved areas through differentiated functional allocation strategies.